Variables

An analylical treatment of the biased proportional navigalion (BPN) is carried oul with lhe aim of optimizing lhe bias parameter. It is shown lhal optimum biasing may lead to significantly more conlrol-effort-efficienl PN guidance in a wide variety of engagement situations, especially lhose involving Ngher target maneuvers. The performance of the BPN is compared wilh lhe standard (unbiased) proporlional navigation (PN) system for the general case of a maneuvering target, and the performance of the BPN is maximized to obtain the optimum bias value. The optimum bias is expressed through a simple algebraic equation which can be readily solved For lhe special (and very useful) case of the effective navigation constant being equal to 3, the equation reduces to a quadratic, leading to an explicil expression for lhe oplinium bias. Specilk exaamples are provided to show the benefits of the BPN law clearly The higher control efficiency of the law is especially useful in extra-atmospheric interception, where the savings in control effort directly translales to a saving of propellent which forms par1 of the payload